Three-dimensional shape reconstruction of 2D landmark points on a single image is a hallmark of human vision, but is a task that has been proven difficult for computer vision algorithms. We define a feed-forward deep neural network algorithm that can reconstruct 3D shapes from 2D landmark points almost perfectly (i.e., with extremely small reconstruction errors), even when these 2D landmarks are from a single image. Our experimental results show an improvement of up to two-fold over state-of-the-art computer vision algorithms; 3D shape reconstruction error (measured as the Procrustes distance between the reconstructed shape and the ground-truth) of human faces is <.004<.004, cars is .0022, human bodies is .022, and highly-deformable flags is .0004. Our algorithm was also a top performer at the 2016 3D Face Alignment in the Wild Challenge competition (done in conjunction with the European Conference on Computer Vision, ECCV) that required the reconstruction of 3D face shape from a single image. The derived algorithm can be trained in a couple hours and testing runs at more than 1,000 frames/s on an i7 desktop. We also present an innovative data augmentation approach that allows us to train the system efficiently with small number of samples. And the system is robust to noise (e.g., imprecise landmark points) and missing data (e.g., occluded or undetected landmark points).

中文翻译：

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一种简单、快速且高精度的算法，可从单个图像上的 2D 地标恢复 3D 形状


单个图像上 2D 标志点的三维形状重建是人类视觉的标志，但事实证明，对于计算机视觉算法来说，这是一项困难的任务。我们定义了一种前馈深度神经网络算法，该算法可以几乎完美地从 2D 地标点重建 3D 形状（即，重建误差极小），即使这些 2D 地标来自单个图像。我们的实验结果表明，与最先进的计算机视觉算法相比，性能提高了两倍；人脸的 3D 形状重建误差（以重建形状与地面实况之间的 Procrustes 距离测量）为 <.004<.004，汽车为 0.0022，人体为 0.022，高度可变形旗帜为.0004。我们的算法还在 2016 年 3D 野外对齐挑战赛（与欧洲计算机视觉会议 ECCV 联合举办）中表现出色，该比赛需要从单个图像重建 3D 脸部形状。导出的算法可以在几个小时内完成训练，并在 i7 桌面上以超过 1,000 帧/秒的速度运行测试。我们还提出了一种创新的数据增强方法，使我们能够使用少量样本有效地训练系统。并且该系统对噪声（例如，不精确的界标点）和丢失数据（例如，被遮挡或未检测到的界标点）具有鲁棒性。